Question

Найдите область определения функции:
а) f(x)=0.5- √x-3
б) f(x)= √2x^2-7x+5
в) f(x)=x-3/4x^2-1
г) f(x)=x/3-x+1/4x^2-9

Answer 1

$1)quad f(x)=0,5-sqrt{x-3}\\OOF:; ; x-3 geq 0; ,; ; x geq 3\\xin [, 3,+infty )\\2); ; f(x)=sqrt{2x^2-7x+5}\\OOF:; ; 2x^2-7x+5 geq 0; ,\\D=9; ,; ; x_1=frac{7-3}{4}=1; ,; ; x_2= frac{7+3}{4}= frac{5}{2}=2,5\\+++[, 1, ]---[2,5]+++ \\xin (-infty ,1, ]cup [, 2,5; ;+infty )$

$3); ; f(x)= frac{x-3}{4x^2-1} \\OOF:; ; 4x^2-1ne 0; ,; ; x^2ne frac{1}{4}; ,; ; xne pm frac{1}{2}\\xin (-infty ,- frac{1}{2})cup (-frac{1}{2},frac{1}{2})cup (frac{1}{2},+infty )\\4); ; f(x)= frac{x}{3-x} +frac{1}{4x^2-9} \\OOF:; ; left { {{3-xne 0} atop {4x^2-9ne 0}} right. ; ; left { {{xne 3} atop {x^2ne frac{9}{4}}} right. ; ; left { {{xne 3} atop {xne pm 1,5}} right. \\xin (-infty ;-1,5)cup (-1,5; ;; 1,5)cup (1,5; ;3)cup (3;+infty )$